Whisk the eggs slightly, and then whisk in the Chevre and milk until smooth. Set aside.
Cook the onion and mushrooms in the butter until tender.
Stir the onion and mushrooms into the Chevre mixture. Add remaining ingredients and stir well.
Bake @ 350° F for 1 hour, stirring occasionally. Check to be sure broccoli is done, cooking 15 minutes more if not.